Nonlinear Dynamics of Energy Harvesting Ocean Buoys

This dissertation looks to investigate different ways that the performance of ocean
energy harvesting buoys can be improved by intentionally inserting nonlinearities
into the system. The goal is to maximize the amount of energy that is extracted from
ocean waves across a broad range of environmental conditions. First, the bifurcation
and stability behavior of inhomogeneous floating bodies is studied. Bifurcation diagrams
and basins of attraction that illustrate the stability of the equilibrium positions
as a function of the vertical position of the center of mass within the body are generated.
Static experiments in still water are conducted to validate these results and dynamic
experiments in a wave flume are carried out to examine how potential well hopping
behavior can be encouraged for various wave conditions.

Next, the gimballed horizontal pendulum is studied for use as an energy harvester
that can be designed for threshold escape behavior rather than the conventional method
of matching frequencies. A nonlinear electromechanical model is developed to study
the system's equilibrium states as a function of tilt angle. A static bifurcation
point is solved for analytically and the implications for an energy harvester, one
that can be designed to jump across stable attractors based on forcing amplitudes,
are discussed. Amplitude sweeps are conducted showing a dynamic bifurcation point
that varies as a function of frequency and effective damping and experiments are run
to validate computational results.

This system is examined further to study how it can be used specifically for harvesting
energy from ocean waves. Threshold escape behavior for parametrically excited systems
with a time dependent term in the potential energy function is discussed and a criterion
is proposed for predicting escape events. Performance metrics are identified to quantify
and compare different responses. Numerical and experimental studies are conducted
showing how the system can be designed for enhanced performance by altering geometric
parameters to suit various excitations. The system's response to both deterministic
single harmonic and stochastic multiharmonic excitations are investigated. Design
implications are discussed.

Then, variable area plate capacitors are studied to determine how topological optimization
can be applied to identify nonintuitive capacitor plate patterning that maximize average
power dissipated through an electrical circuit during energy harvesting. Coupled electromechanical
equations of motion are derived that include both the instantaneous and change in
overlapping conductive area as functions of plate rotation. A genetic algorithm is
used to optimize these terms and then map them to physical plate configurations. The
results obtained apply specifically to the case presented, however the methods are
general and can be used to solve a broad range of electrostatic energy harvesting
problems.

Finally, an analytical method is developed to determine the instances in time to stroboscopically
sample the response of a dynamical system subject to varying input excitations. The
simplest case of a linear frequency sweep is first considered before generalizing
to include more complex functions with nonlinear sweep rates and arbitrary phase shifts.
This method improves the accuracy of various simulation results throughout this dissertation
but can be extended to aid the analysis of any generic dynamical system.